Write an equation of a line passing through (2, 5), perpendicular to x−5y=−10

Kamila Frye
2022-10-16
Answered

Write an equation of a line passing through (2, 5), perpendicular to x−5y=−10

You can still ask an expert for help

Kaylee Evans

Answered 2022-10-17
Author has **20** answers

Let's first look at the the line x−5y=−10 and solve it for y so that we can put it into the slope-intercept form, the general form of which is:

y=mx+b, where m= slope and b= y-intercept.

$x-5y=-10$

$5y=x+10$

$y=\frac{1}{5}x+2$

And so slope, $m=\frac{1}{5}$

To find the perpendicular slope, we take the negative inverse, which gives us m=−5.

To find the line passing through the point (2,5) with slope −5, we can use the point slope form, which has as a general form:

$y-{y}_{1}=m(x-{x}_{1})$ where $x}_{1},{y}_{1$ are a point. So we have:

(y−5)=−5(x−2)

For comparison, let's put this into slope-intercept form:

y=−5x+15

y=mx+b, where m= slope and b= y-intercept.

$x-5y=-10$

$5y=x+10$

$y=\frac{1}{5}x+2$

And so slope, $m=\frac{1}{5}$

To find the perpendicular slope, we take the negative inverse, which gives us m=−5.

To find the line passing through the point (2,5) with slope −5, we can use the point slope form, which has as a general form:

$y-{y}_{1}=m(x-{x}_{1})$ where $x}_{1},{y}_{1$ are a point. So we have:

(y−5)=−5(x−2)

For comparison, let's put this into slope-intercept form:

y=−5x+15

asked 2021-06-01

Find the linear approximation of the function

Use L(x) to approximate the numbers

asked 2022-11-04

Find the slope of any line perpendicular to the line passing through (44,35) and (−2,−3)

asked 2022-09-02

How many forms of linear equations are there?

asked 2022-09-23

The larger of 2 numbers is 5 less than 5 times the smaller number. The sum of the two numbers is 61. What are the two numbers?

asked 2022-10-15

Find a line that passes through (3,5) perpendicular to a line whose slope is -1/9

asked 2022-11-11

The length of a rectangular garden is 5 less than two times the width. There is a 5 foot wide sidewalk on 2 sides that has an area of 225 sq ft. How do you find the dimensions of the garden?

asked 2022-09-06

Find the equation of the line that passes through the point (0,2) and perpendicular to the line x-y=6